Lab Manual: Resistors in Parallel | Lab Manuals for Class 10 PDF Download

Objective

Materials Required
Two standard resistance coils (or resistors), ammeter (0-1.5 A), voltmeter (0-1.5 V), one-way plug key, a low resistance rheostat, connecting wires, a piece of sand paper and cell or battery eliminator.

Theory/ Principle

As shown in Fig. 1, two resistors of resistances R1 and R2 are connected between two points A and B in parallel combination. Let the potential difference applied by the DC source to this combination be V.
Let I₁ and I₂ be the currents measured by an ammeter, connected in series with each resistor R₁ and R₂ respectively, then

I = I₁ + I₂ …….(i)
According to Ohm’s law,
I₁ = V/R₁ and I₂ = V/R₂   .......(ii)
If R_p is the equivalent resistance of the given parallel combination, having the same potential difference as the applied potential, then
I  = V/R_p   ......(iii)
From Eqs. (i), (ii) and (iii), we get

or

or

Therefore, when number of resistances are connected in a parallel combination, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

Procedure

• Note down the least count and zero error (if any) of the given ammeter and voltmeter.
• Clean the ends of connecting wires using sand paper.
• Find the values of two given resistances R₁ and R₂ by the procedure given in Experiment 5
  
• Connect the given resistors in parallel combination between the two terminals of the voltmeter (as shown in Fig. 3).
  
  Fig. 3 (a) Circuit diagram for resistors in parallel

Fig. 3 (b) Block diagram for resistors in parallel

• Put the plug in the key and take the readings of ammeter and voltmeter (as done in Experiment 5).
• Repeat the step 5 three times by changing the position of the sliding contact of the rheostat (as done in Experiment 5).
• Tabulate the readings and find the ratio of V and I. It will give the equivalent resistance of the combination.

Observation

• Least count of ammeter = ………… A
• Zero error of ammeter = ………….. A
• Least count of voltmeter = ………. V
• Zero error of voltmeter = …………. V
• Zero correction in ammeter reading = ……….. A
• Zero correction in voltmeter reading = ………… V
  

Calculations

• Mean value of R₁ = ……….. Ω
• Mean value of R₂ = ………. Ω
  Equivalent value of parallel combination,
  • By calculations,
  • By experiment, Rp = …………. Ω

Result

• The equivalent resistance of parallel combination, R_p = ………….. Ω
• There is close agreement between the calculated value and the value obtained by the experiment. Hence, 1/R_p = 1/R₁ + 1/R₂ is verified.

Percentage Error

It shows that percentage error is within the experimental error.

Precautions

• It is to be properly checked that ammeter is connected in series and voltmeter is connected in parallel.
• The connecting wires should be thick and must have tight connection at joints.
• The ends of connecting wires should be cleaned properly using sand paper.
• The ammeter and voltmeter must be of proper range and of less least count.
• Current should be passed for very short time, otherwise heating effect can change the actual result.

Sources of Error

• Reading error may be possible while observing the pointer of ammeter and voltmeter.
• Thick connecting wires may not be available at the time of performing the experiment.
• Area of cross-section of resistance may not be uniform across the length of wire.
• The high resistance rheostat may be used.
• Current may be allowed for longer period.
• The terminal screws of the instruments may not be tightened properly.